[en] Designing optimized ECR (electron cyclotron resonance) ion beam sources can be streamlined by the accurate simulation of beam optical properties in order to predict ion extraction behavior. The complexity of these models, however, can make PIC-based simulations time-consuming. In this paper, we first describe a simple kinetic plasma finite element simulation of extraction of a proton beam from a permanent magnet hexapole ECR ion source. Second, we analyze the influence of secondary electrons generated by ion collisions in the residual gas on the space charge of a proton beam of a dual-solenoid ECR ion source. The finite element method (FEM) offers a fast modeling environment, allowing analysis of ion beam behavior under conditions of varying current density, electrode potential, and gas pressure. The new version of SCALA/TOSCA v14 permits the making of simulations in tens of minutes to a few hours on standard computer platforms without the need of particle-in-cell methods. The paper is followed by the slides of the presentation. (authors)